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Consonance And Dissonance





CONSONANCE


Consonance has been defined variously through:
  • Frequency ratios: with ratios of lower simple numbers being more consonant than those which are higher (Pythagoras). Many of these definitions do not require ''exact'' integer tunings, only approximation.

  • --- Coincidence of harmonics: with consonance being a greater coincidence of Harmonic s or Partial s (collectively Overtone s) (Helmholtz, 1877/1954). By this definition consonance is dependent not only on the quality of the interval between two notes, but on the combined spectral distribution and thus sound quality ( Timbre ) of the harmonic interval (see the entry under Critical Band ).

  • --- Fusion or pattern matching: fundamentals may be perceived through pattern-matching of the separately analyzed partials to a best-fit exact-harmonic template (Gerson & Goldstein, 1978) or the best-fit subharmonic (Terhardt, 1974). Or harmonics may be perceptually fused into one entity, with consonances being those intervals which are more likely to be mistaken for unisons, the perfect intervals, because of the multiple estimates of fundamentals, at perfect intervals, for one harmonic tone (Terhardt, 1974). By these definitions inharmonic partials of otherwise harmonic spectra are usually processed separately (Hartmann et al., 1990), unless frequency or amplitude modulated coherently with the harmonic partials (McAdams, 1983). For some of these definitions neural-firing supplies the data for pattern-matching, see directly below (e.g., Moore, 1989; pp.183-187; Srulovicz & Goldstein, 1983).

  • --- Period length or neural-firing coincidence: with the length of periodic neural-firing created by two or more wave-forms, lower simple numbers creating shorter or common periods or higher coincidence of neural-firing and thus consonance (Patternson, 1986; Boomsliter & Creel, 1961; Meyer, 1898; Roederer, 1973, p.145-149). Pure tones cause neural-firing exactly with the period or some multiple of the pure tone.


In what is now called the Common Practice Period consonant intervals include:


Polyphonic Cadence he first an imperfect consonance on a weak beat, the second a perfect consonance on a strong beat, such as a major sixth moving to an octave (for instance, the major (imperfect) sixth D-B followed by the perfect octave C-C').


DISSONANCE


In Music , dissonance is the quality of sounds which seems "unstable", and has an aural "need" to " Resolve " to a "stable" Consonance . Both consonance and dissonance are words applied to Harmony , Chord s, and Interval s and by extension to Melody , Tonality , and even Rhythm and Metre . Although there are important physical and neurological facts important to understanding the idea of dissonance, the precise definition of dissonance is culturally conditioned — definitions of and conventions of usage related to dissonance vary greatly among different musical styles, traditions, and cultures. Nevertheless, the basic ideas of dissonance, consonance, and resolution exist in some form in all musical traditions that have a concept of melody, harmony, or tonality.

Additional confusion about the idea of dissonance is created by the fact that musicians and writers sometimes use the word ''dissonance'' and related terms in a precise and carefully defined way, more often in an informal way, and very often in a metaphorical sense ("rhythmic dissonance"). For many musicians and composers, the essential ideas of dissonance and resolution are vitally important ones that deeply inform their musical thinking on a number of levels.

Despite the fact that words like "unpleasant" and "grating" are often used to explain the sound of dissonance, in fact all music with a harmonic or tonal basis — even music which is perceived as generally harmonious — incorporates some degree of dissonance. The buildup and release of tension (dissonance and resolution), which can occur on every level from the subtle to the crass, is to a great degree responsible for what many listeners perceive as beauty, emotion, and expressiveness in music.


Dissonance and musical style


Understanding a particular musical style's treatment of dissonance — what is considered dissonant and what rules or procedures govern how dissonant intervals, chords, or notes are treated — is key in understanding that particular style. For instance, in the Common Practice Period , harmony is generally governed by chords, which are collections of notes generally considered to be consonant (though even within this harmonic system there is a hierarchy of chords, with some considered relatively more consonant and some relatively more dissonant). Any note that does not fall within the prevailing harmony is considered dissonant. Particular attention is paid to how dissonances are approached (approach by step is less jarring, approach by leap more jarring), even more to how they are resolved (almost always by step), to how they are placed within the meter and rhythm (dissonances on stronger beats are considered more forceful and those on weaker beats less vital), and to how they lie within the phrase (dissonances tend to resolve at phrase's end). In short, dissonance is not used willy-nilly but is used in a very careful, controlled, and well-circumscribed way. The subtle interplay of different levels of dissonance and resolution is vital to understanding the tonal and harmonic language of this period.


Dissonance throughout the history of western music


Dissonance has been understood and heard differently in different musical traditions, cultures, styles, and time periods.

Relaxation and tension have been used as analogy since the time of Aristotle till the present (DeLone et al. 1975, p.290).

In early Renaissance Music intervals such as the perfect fourth were considered strong dissonances that must be immediately resolved. The ''regola delle terze e seste'' ("rule of sixths and thirds") required that imperfect consonances should resolve to a perfect one by a half step progression in one voice and a whole step progression in another (Dahlhaus 1990 , p.179). Anonymous 13 allowed two or three, the ''Optima intorductio'' three or four, and Anonymous 11 ( 15th Century ) four or five successive imperfect consonances. By the end of the 15th century imperfect consonances were no longer "tension sonorities" but, as evidence by the allowance of their successions argued for by Adam Von Fulda , but independent sonorities, according to Gerbert (vol.3, p.353), "Although older scholars once would forbid all sequences of more than three or four imperfect consonances, we who are more modern allow them." (ibid, p.92)

In the Common Practice Period all dissonances were required to be Prepared and then Resolved , occurring on weak beats and quickly giving way or returning to a consonance. There was also a distinction between Melodic and Harmonic dissonance. Dissonant melodic intervals then included the Tritone and all Augmented and Diminished intervals. Dissonant harmonic intervals included:


Thus, Western musical history can be seen as starting with a quite limited definition of consonance and progressing towards an ever wider definition of consonance. Early in history, only intervals low in the Overtone Series were considered consonant. As time progressed, intervals ever higher on the overtone series were considered consonant. The final result of this was the so-called " Emancipation Of The Dissonance " (the words of Arnold Schoenberg ) by some 20th-century composers. Early 20th-century American composer Henry Cowell viewed Tone Cluster s as the use of higher and higher overtones.

Despite the fact that this idea of the historical progression towards the acceptance of ever greater levels of dissonance is somewhat oversimplified and glosses over important developments in the history of western music, the general idea was attractive to many 20th-century modernist composers and is considered a formative Meta-narrative of Musical Modernism .

One example of imperfect consonances previously considered dissonances in Guillaume De Machaut 's "Je ne cuit pas qu'onques":

One example of baroque dissonance:

One example of classical era dissonance:

One example of modernist dissonance:


The objective (physical/physiological) basis of dissonance


Musical styles are similar to languages, in that certain physical, physiological, and neurological facts create bounds that greatly affect the development of all languages. Nevertheless, different cultures and traditions have incorporated the possibilities and limitations created by these physical and neurological facts into vastly different, living systems of human language. Neither the importance of the underlying facts, nor the importance of the culture in assigning a particular meaning to the underlying facts, should be minimized.

For instance, two notes played simultaneously but with slightly different frequencies, produce a Beating "wah-wah-wah" sound that is very audible. Some musical styles consider this effect to be objectionable ("out of tune") and go to great lengths to eliminate it. Other musical styles consider this sound to be an attractive part of the musical timbre and go to equally great lengths to create instruments that have this slight "roughness" as a feature of their sound (Vassilakis, 2005).

Sensory dissonance and its two perceptual manifestations ( Beating and roughness) are both closely related to a sound signal's amplitude fluctuations. Amplitude fluctuations describe variations in the maximum value (amplitude) of sound signals relative to a reference point and are the result of wave interference. The interference principle states that the combined amplitude of two or more vibrations (waves) at any given time may be larger (constructive interference) or smaller (destructive interference) than the amplitude of the individual vibrations (waves), depending on their phase relationship. In the case of two or more waves with different frequencies, their periodically changing phase relationship results in periodic alterations between constructive and destructive interference, giving rise to the phenomenon of amplitude fluctuations.

Amplitude fluctuations can be placed in three overlapping perceptual categories related to the rate of fluctuation. Slow amplitude fluctuations (≈≤20 per second) are perceived as loudness fluctuations referred to as beating. As the rate of fluctuation is increased, the loudness appears to be constant and the fluctuations are perceived as “fluttering” or roughness. As the amplitude fluctuation rate is increased further, the roughness reaches a maximum strength and then gradually diminishes until it disappears (≈≥75-150 fluctuations per second, depending on the frequency of the interfering tones).